OFFSET
1,3
FORMULA
Given g.f. A(x), then G(x) = d/dx A(x^8)/(4*x^4) = Sum_{n>=1} (2*n-1)*a(n)*x^(8*n-5) is the g.f. of A212425 and satisfies: G(x) = (x + G(G(x)))^3.
EXAMPLE
G.f.: A(x) = x + x^2 + 6*x^3 + 58*x^4 + 704*x^5 + 9765*x^6 + 147870*x^7 +...
Let G(x) = d/dx A(x^8)/(4*x^4), then G(x) = (x + G(G(x)))^3, where
G(x) = x^3 + 3*x^11 + 30*x^19 + 406*x^27 + 6336*x^35 + 107415*x^43 +...
G(G(x)) = x^9 + 9*x^17 + 117*x^25 + 1788*x^33 + 29925*x^41 + 530910*x^49 +...
PROG
(PARI) {a(n)=local(G=x^3+3*x^11); for(i=1, n, G=(x+subst(G, x, G +O(x^(8*n))))^3); polcoeff(G, 8*n-5)/(2*n-1)}
for(n=1, 30, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, May 16 2012
STATUS
approved